获取根节点松弛解

Question

I'm working on a B&C framework in Gurobi/Python and I would like retrieve the optimal solution of the root node problem. How can I do that?.

Thanks.

Answer 1

Most likely we will want to use a MIPNODE callback . Note that the MIPNODE callback will be called once for each cut pass during the root node solve. The MIPNODE_NODCNT value will remain at 0 until the root node is complete. If you query relaxation values from during the root node, the first MIPNODE callback will give the relaxation with no cutting planes, and the last will give the relaxation after all root cuts have been applied.

Here is an example that queries the relaxation solution at each cut pass at the root node (to compute the objecive value, for illustration purpose), and quits the optimization after the root node is completed.

import sys
from gurobipy import *

def mycallback(model, where):
    if where != GRB.Callback.MIPNODE:
        return

    nodecount = model.cbGet(GRB.Callback.MIPNODE_NODCNT)
    if nodecount > 0:
        print("Root node completed, terminate now")
        model.terminate()
        return

    if model.cbGet(GRB.Callback.MIPNODE_STATUS) == GRB.Status.OPTIMAL:
        x = model.cbGetNodeRel(model._vars)
        objval = 0.0
        for idx, c in enumerate(model._coef):
            objval += x[idx] * c

        print(f"Root relaxation value: {objval}")

if len(sys.argv) < 2:
    print('Usage: callback.py filename')
    quit()

model = read(sys.argv[1])
model._vars = model.getVars()
model._coef = [v.obj for v in model._vars]
model.Params.OutputFlag = 0
model.optimize(mycallback)

If you run the above code with the example model p0033.mps (distributed along with the examples in the Gurobi installation), you should see:

Read MPS format model from file /Library/gurobi811/mac64/examples/data/p0033.mps
Reading time = 0.00 seconds
P0033: 16 rows, 33 columns, 98 nonzeros
Root relaxation value: 2839.4918382913806
Root relaxation value: 2941.4
Root relaxation value: 2952.0
Root relaxation value: 2953.325
Root relaxation value: 2966.7142857142853
Root relaxation value: 2972.0083333333337
Root relaxation value: 2973.171211242146
Root relaxation value: 3023.0025940337223
Root relaxation value: 3033.999999999998
Root relaxation value: 3056.7500000000005
Root relaxation value: 3057.8333333333335
Root relaxation value: 3057.8333333333335